摘要
分析了刚度和阻尼并存的一般边界条件下线弹性杆与刚体的纵向碰撞过程,得到了碰撞后第一个波动周期杆振动的位移、速度和应力的解析表达式,讨论了碰撞持续时间为2倍杆长与波速比的条件.将导出的解析表达式通过具体的算例代入计算,讨论了不同质量比、不同连接刚度条件下连接阻尼对于碰撞过程中杆中质点速度及应力响应的影响.研究表明,连接阻尼改变了受碰撞弹性杆的振动模式,连接阻尼影响着碰撞反射波速度和应力的突变幅度;连接阻尼增大,杆中速度和应力响应分布变平缓;在连接刚度较大的情况下,连接阻尼变化对于杆中质点速度和应力影响较大;碰撞持续时间与质量比、连接刚度、连接阻尼及杆长有关,与碰撞的初速度无关;在质量比较大的情况下,连接阻尼使得反射波到达杆碰撞端时,杆端的应力有显著的变化.
The longitudinal impact between a rigid body and an elastic rod with boundary stiff- ness and damping conditions was discussed, the analytical velocity and stress distributions dur- ing the 1st impact wave period were derived for the rod, and the condition that the impact time duration equals 2 times of the value of the rod length divided by the wave velocity, was also in- vestigated. Then several examples were calculated to discuss the effects of the boundary damp- ing on the velocity and stress distributions in the rod in the cases of different mass ratios be- tween the rigid body and the rod, and different connection stiffnesses. It is shown that the boundary damping influences the values of reflection wave velocity and stress wave front, and the velocity and stress distributions in the rod become gentler with a higher boundary damping. Given a larger boundary stiffness, the effects of the boundary damping on the velocity and stress in the rod will be more significant. It is also indicated that the impact time duration is not related to the initial impact velocity, but to the mass ratio, the boundary stiffness, the bounda- ry damping and the rod length. Especially, for a larger mass ratio, the boundary damping has greater influence on the stress of the rod＇ s impact end.
出处
《应用数学和力学》
CSCD
北大核心
2015年第4期393-403,共11页
Applied Mathematics and Mechanics
关键词
弹性杆
纵向碰撞
连接阻尼
波动分析法
elastic rod
longitudinal impact
boundary damping
wave propagation analysis
